Learn some patterns for organizing research code and computations (Muthiah)

Come up with general framework for constructing sub-Hopf algebras of Malvenuto-Reutenauer that arise from lattice quotients on the weak order (see: Nathan Reading, Lattice congruences, fans and Hopf algebras, http://arxiv.org/abs/math/0402063). (Dilks)

Abstracts

Monday

Franco Saliola

Let's Start Using Sage!

A whirlwind tour of what Sage can and cannot do (and why you should care).

Stephen Doty

Getting Started with the Sagemath Cloud

Sagemath Cloud is a recent project to make Sage (and much more: e.g., Python, R, LaTeX, Terminal) available in any modern browser, without the need to install anything on the computer. This will be an introduction, with no prerequisites.

Dinakar Muthiah

MV polytopes in finite and affine type

MV polytopes provide a model for highest weight crystals in finite and affine type. Interest in MV polytopes comes from the variety of different contexts in which they appear: MV cycles in the affine Grassmannian, irreducible components in preprojective varieties, character-support for KLR modules, and PBW bases. They also can be constructed purely combinatorially. I will focus on the combinatorics of MV polytopes and briefly mention the other contexts in which they appear. I will also discuss the MV polytope code that we have already written and explain some of the tasks that remain.

Nantel Bergeron

Homogeneous, Non-commutative Gröbner Bases

Computing a non-commutative Gröbner basis takes an extremely long time. I will present the algorithm and indicate where it could be parallelized...

Tuesday

Anne Schilling

Algebraic Combinatorics in Sage: How to use it, make it, and get it into Sage

We will very briefly discuss the history of combinatorics in Sage and give some examples on how to use some features like crystals, permutations and words. We will then implement some new missing features together and see how to get them into Sage.

Mark A. & George T.

Code collaboration in SAGE and other open source projects

We will have a brief introduction to the typical organizational structures and technologies used by large-scale open source projects and how one can contribute at various levels in each. This will be followed by a tutorial for working collaboratively on code to contribute directly to the SAGE environment.

Mike Zabrocki

How to program a combinatorial Hopf algebra (with bases)

I will review the structure of the code for combinatorial Hopf algebras (symmetric functions/partitions, quasi-symmetric functions/compositions, non-commutative symmetric functions/compositions, symmetric functions in non-commuting variables/set partitions) that are already in Sage and explain how to create a new combinatorial Hopf algebra on another set of combinatorial objects. I will also point out the ongoing work on open tickets to implement other combinatorial Hopf algebras (packed words #15611, FQSym, WQSym, PQSym #13793, PBT/Loday-Ronco #13855)

Wednesday

Ben Salisbury

Affine crystals in Sage

I will give a brief overview of affine crystals (both irreducible highest weight affine crystals and affine Verma crytals) before discussing certain implementations of these crystals in Sage. I will also point to some current Sage work in this area as well as possible extensions beyond.

Peter T. & Emily P.

Linear Algebra in Sage

We will lead a session on figuring out how to get sage to do something. This will mostly consist of participants working together to try and figure stuff out. That stuff will be from linear algebra and, if things go well, random matrix theory.

Thursday

Simon King

An F5 algorithm for modules over path algebra quotients and the computation of Loewy layers

The F5 algorithm is a signature based algorithm to compute Gröbner bases for modules over polynomial rings. The F5 signature allows to exploit commutativity relations in order to avoid redundant computations. When considering modules over path algebra quotients, one can instead exploit the quotient relations to avoid redundancies.

For my applications, it is important that Gröbner bases are actually not more than a by-product of the F5 algorithm. Indeed, the F5 signature provides additional information: If the quotient algebra is a basic algebra and if a negative degree monomial ordering is used, then the F5 signature allows to read off the Loewy layers of the module.

Aaron Lauve

Convolution Powers: step by step

I share my personal story (I want to say "natural progression" but I'm sure it's nothing of the kind) from perceived gap in the Sage code for Hopf algebras to sage-trac ticket submission.

George Seelinger

Orthogonal Idempotents in Semisimple Brauer Algebras

I will describe my joint work with Doty and Lauve. Using Sage, we found a recursive description of primitive, pairwise orthogonal idempotents in a semisimple Brauer algebra. These are analogous to Young's seminormal idempotents for group algebras of the symmetric groups.

Jonathan Judge

Root Multiplicities for Kac-Moody Algebras in Sage

Root multiplicities are fundamental data in the structure theory of Kac-Moody algebras. We will give a brief survey on root multiplicities that highlights the differences between finite, affine, and indefinite types. Then we will describe the two main ways that these multiplicities are computed, namely Berman-Moody's formula and Peterson's recurrent formula. Lastly, we demonstrate an implementation of Peterson's recurrent formula in Sage.

Collaborative Development with Git-Trac: documentation that explains how to use the helper git trac command, which simplifies many of the most common actions in collaboration on Sage (checking out a ticket; pulling new changes; pushing your changes; ...)